A Family of Bayesian Estimators for the Two-Parametric Burr Type II Distribution

This study discusses the posterior estimation for the parameters of the Burr type II distribution (BIID). The informative and noninformative priors along with different loss functions have also been assumed for the posterior estimation. The applicability of the proposed distribution has also been discussed. The modeling capability of the proposed model has been compared with seven classes of the lifetime distributions using real data. The generalizations of Weibull, exponential, Rayleigh, gamma, log normal, Pareto, Maxwell, Levy, Laplace, inverse gamma, Gompertz, chi-square, inverse chi-square, half normal, and log-logistic distributions have been considered for the comparison. The comparison has been made based on different goodness-of-fit criteria, such as Akaike information criteria (AIC), Bayesian information criteria (BIC), and Kolmogorov-Smirnov (KS) test. Based on the results from the study, it can be suggested that the BIID can efficiently replace commonly used lifetime distributions and their modifications. The results under this model were comparable with different conventional/modified distributions having up to six parameters.

Design of SkSP-R Plan for Popular Statistical Distributions

The design of a Skip-lot sampling plan of type SkSP-R is presented for time truncated life test for the Weibull, Exponentiated Weibull, and Birnbaum-Saunders lifetime distributions. The plan parameters of the SkSP-R plan under these three distributions are determined through a nonlinear optimization problem. Tables are also constructed for each distribution. The advantages of the proposed plan over the existing sampling schemes are discussed. Application of the proposed plan is explained with the help of an example. The Birnbaum-Saunders distribution is economically superior to other two distributions in terms of minimum average sample number.

The gompertz exponential pareto distribution with the properties and applications to bladder cancer and hydrological datasets

Many existing distributions in literatures does not have the modeling fits capacity to adequately describe the real-life phenomena. The Exponential Pareto (EP) distribution has further gained some generalizations among several authors using different generator techniques with an aim to obtain a new distribution with greater flexibility. This article proposes Gompertz Exponential Pareto (GEP) distribution using the Gompertz generator. Findings from the study revealed some lifetime distributions as special cases and mathematical properties of the distribution investigated including the mean, variance, coefficient of variation, quantile, moment, moment generating function and, order statistics. The distribution can be positively or negatively skewed. It is unimodal with failure rates whose shapes could be reversed J bathtub, constant, decreasing and, increasing and the parameters were estimated using maximum likelihood estimation approach. Applications to two real-life datasets revealed the ability of GEP distribution to provide more flexibilities and better fit to the dataset compared to some previously proposed distributions for the data. The results also revealed that GEP had the superior performance over other generalizations of EP distribution existing in literatures and the performance has further strengthened the usefulness of the Gompertz-generator technique.

Lifetime Distribution of Clusters in Binary Mixtures Involving Hydrogen Bonding Liquids

Hydrogen bonded liquids are associated liquids and tend to exhibit local inhomogeneity in the form of clusters and segregated sub-nano domains. It is an open question as to whether Hbonded clusters in pure water have common features with the water segregated pockets observed in various aqueous binary mixtures, such as water-alcohol mixtures, for example. In the present study, we demonstrate through classical molecular dynamics studies of the lifetime distributions of the hydrogen bonds in different types of binary mixtures, that these lifetimes exhibit the same universal features in the case of the pure liquids, independently of the species concentrations. The same types of three distinct lifetimes are observed, all of them in the sub picosecond regime. The primary lifetime concerns that of Hbonded dimers, and strongly depends on Hbonding criteria such as the bonding distance. The two others are independent of bonding criteria. The secondary lifetime concerns Hbonded cluster lifetimes, while the tertiary lifetime concerns the topology of these clusters, such as chains or globules, for example. This surprizing separation in three distinct lifetimes suggests the existence of associated three distinct kinetic mechanisms in the very short sub-picosecond time scales.

An Inferential Aptness of a Weibull Generated Distribution and Application

In this article an attempt has been made to develop a flexible single parameter continuous distribution using Weibull distribution. The Weibull distribution is most widely used lifetime distributions in both medical and engineering sectors. The exponential and Rayleigh distribution is particular case of Weibull distribution. Here in this study we use these two distributions for developing a new distribution. Important statistical properties of the proposed distribution is discussed such as moments, moment generating and characteristic function. Various entropy measures like Rényi, Shannon and cumulative entropy are also derived. The kthkt⁢h order statistics of pdf and cdf also obtained. The properties of hazard function and their limiting behavior is discussed. The maximum likelihood estimate of the parameter is obtained that is not in closed form, thus iteration procedure is used to obtain the estimate. Simulation study has been done for different sample size and MLE, MSE, Bias for the parameter λλ has been observed. Some real data sets are used to check the suitability of model over some other competent distributions for some data sets from medical and engineering science. In the tail area, the proposed model works better. Various model selection criterion such as -2LL, AIC, AICc, BIC, K-S and A-D test suggests that the proposed distribution perform better than other competent distributions and thus considered this as an alternative distribution. The proposed single parameter distribution is found more flexible as compare to some other two parameter complicated distributions for the data sets considered in the present study.

EB3-informed dynamics of the microtubule stabilizing cap during stalled growth

Microtubule stability is known to be governed by a stabilizing GTP/GDP-Pi cap, but the exact relation between growth velocity, GTP hydrolysis and catastrophes remains unclear. We investigate the dynamics of the stabilizing cap through in vitro reconstitution of microtubule dynamics in contact with micro-fabricated barriers, using the plus-end binding protein GFP-EB3 as a marker for the nucleotide state of the tip. The interaction of growing microtubules with steric objects is known to slow down microtubule growth and accelerate catastrophes. We show that the lifetime distributions of stalled microtubules, as well as the corresponding lifetime distributions of freely growing microtubules, can be fully described with a simple phenomenological 1D model based on noisy microtubule growth and a single EB3-dependent hydrolysis rate. This same model is furthermore capable of explaining both the previously reported mild catastrophe dependence on microtubule growth rates and the catastrophe statistics during tubulin washout experiments.

If Loud Aliens Explain Human Earliness, Quiet Aliens Are Also Rare

If life on Earth had to achieve n “hard steps“ to reach humanity's level, then the chance of this event rose as time to the nth power. Integrating this over habitable star formation and planet lifetime distributions predicts >99% of advanced life appears after today, unless n < 3 and max planet duration <50 Gyr. That is, we seem early. We offer this explanation: a deadline is set by loud aliens who are born according to a hard steps power law, expand at a common rate, change their volume appearances, and prevent advanced life like us from appearing in their volumes. Quiet aliens, in contrast, are much harder to see. We fit this three-parameter model of loud aliens to data: (1) birth power from the number of hard steps seen in Earth’s history, (2) birth constant by assuming a inform distribution over our rank among loud alien birth dates, and (3) expansion speed from our not seeing alien volumes in our sky. We estimate that loud alien civilizations now control 40%–50% of universe volume, each will later control ∼ 105–3 × 107 galaxies, and we could meet them in ∼200 Myr–2 Gyr. If loud aliens arise from quiet ones, a depressingly low transition chance (<∼10−4 ) is required to expect that even one other quiet alien civilization has ever been active in our galaxy. Which seems to be bad news for the Search for Extraterrestrial Intelligence. But perhaps alien volume appearances are subtle, and their expansion speed lower, in which case we predict many long circular arcs to find in our sky.

Inference for One-Shot Devices with Dependent k-Out-of-M Structured Components under Gamma Frailty

A device that performs its intended function only once is referred to as a one-shot device. Actual lifetimes of such kind of devices under test cannot be observed, and they are either left-censored or right-censored. In addition, one-shot devices often consist of multiple components that could cause the failure of the device. The components are coupled together in the manufacturing process or assembly, resulting in the failure modes possessing latent heterogeneity and dependence. In this paper, we develop an efficient expectation–maximization algorithm for determining the maximum likelihood estimates of model parameters, on the basis of one-shot device test data with multiple failure modes under a constant-stress accelerated life-test, with the dependent components having exponential lifetime distributions under gamma frailty that facilitates an easily understandable interpretation. The maximum likelihood estimate and confidence intervals for the mean lifetime of k-out-of-M structured one-shot device under normal operating conditions are also discussed. The performance of the proposed inferential methods is finally evaluated through Monte Carlo simulations. Three examples including Class-H failure modes data, mice data from ED01 experiment, and simulated data with four failure modes are used to illustrate the proposed inferential methods.